They bemoaned his loss but were proud he had been picked to lead where, as Mr. Carney himself put it, the challenges were greatest. Now the time has come for him to deliver. He picks up the reins today. Here are five big things in his inbox.

1. The Economy

Britain’s economy has barely budged since 2010 and official data published last week showed it was 3.9% smaller at the end of March than it was five years earlier, just before the onset of recession.That’s a much worse performance than the U.S., Germany and Mr. Carney’s native Canada.

Economists bicker over whether Treasury chief George Osborne’s austerity drive is to blame, or whether it’s the fallout from the euro zone debt crisis, a crippled banking system, an inflationary squeeze on consumers or some combination of the above.

Whatever ails the U.K., Mr. Osborne and Prime Minister David Cameron are expecting Mr. Carney to deliver the durable recovery that has eluded them. He has to do that without setting off inflation again, which has been more of a problem in Britain over the last five years than elsewhere.

2. Forward Guidance

If Mr. Carney were joining a fashionable London restaurant as head chef, this would presumably be his signature dish. Mr. Carney was an early advocate of central bank commitments to keep rates low until economies are well on the road to recovery.

The theory goes that, disabused of any worries that rates may shoot up in the short term, companies and households will spend and invest. The Federal Reserve under Ben Bernanke has made use of policy guidance tied to economic thresholds (the Fed has vowed not to touch rates until unemployment drops to 6.5%), a form many economists expect Mr. Carney to emulate in the U.K.

There was no love lost between Britain’s bankers and retiring governor Mervyn King, who loathed what he viewed as their special pleading and wasn’t shy about saying so. Mr. Carney’s former career at Goldman Sachs suggests he might be more on the City of London’s wavelength. But any banker hoping for an easing of relentless regulatory demands for more capital is surely likely to be disappointed. Mr. Carney may be more willing to have them over for lunch at BOE headquarters on Threadneedle Street, but, as head of the Financial Stability Board, he is unlikely to tolerate any slippage in U.K. regulatory standards. Nor, since he is only here for five years, is he going to permit a bank to get itself into such a mess it risks hurting the system.

4. Reform of the Bank of England

Lawmakers on parliament’s powerful Treasury Select Committee have made it crystal clear they want a more open, accountable and transparent Bank of England, and the new governor may not wish to risk their ire by leaving the Old Lady, as its affectionately known, unreformed. Two more immediate challenges are who to get to fill the shoes of deputy governor Paul Tucker, who leaves in the fall, and deputy governor Charles Bean, who leaves next year after agreeing to delay retirement to help Mr. Carney settle in. Queen Elizabeth II and the treasury are the ones who officially give the nod, but Mr. Carney will surely want a say.

5. Constructing a Ringfence

Mr. Carney must also oversee the construction of a ringfence that lawmakers have demanded to separate banks’ retail operations from their investment banking arms. The legislation is still trundling through parliament. Mr. Carney and his banking supervisors at the BOE’s Prudential Regulation Authority will have the difficult task of implementing it.